It's been a long time since I used Debian, but...
Check "/etc/network/interfaces" for content
It should contain something like:
iface eth0 inet static
And a similar configuration for eth1.
If the file is empty, or only contains the example config, you should change it to something like the above.
After you have done this, you might have to add the interfaces to the default runlevel ("rc-update add net.eth0 default" in Gentoo, don't remember how in debian). This might require you to add a symbolic link from /etc/init.d/net.lo --> /etc/init.d/net.ethX, but again, this is the Gentoo way.
If the above is not helpful, I'd check this page: http://wiki.debian.org/NetworkConfiguration
Alternatively there might be a problem with the network driver in debian, or the setup in vmware (change NIC hardware emulation?).
Haven't used VMWare Fusion, so can't really tell you anything constructive without more info there. But if it is anything like VirtualBox, you can specify NIC emulation, or use the actual hardware. The latter requires Debian to actually have the NIC driver installed (for your spesific network card).
But the fact that you can list interfaces with "ifconfig -a" suggests that the problem is a config problem in debian, and not a VMWare related problem (at this point).